Advanced Calculus

Advanced Calculus includes some topics such as infinite series, power series, and so on which are all just the application of the principles of some basic calculus topics such as differentiation, derivatives, rate of change and o on. The important areas which are necessary for advanced calculus are vector spaces, matrices, linear transformation. Advanced Calculus helps us to gain knowledge on a few important concepts such as

• Quadratic forms
• Generalized Stokes theorem
• Vector fields as derivatives
• Integration of forms
• Multilinear algebra
• Continuous differentiability
• Tangent space and normal space via gradients
• Dual space and dual basis
• Critical point analysis for multivariate functions, etc.